Nuprl Lemma : fun_exp_unroll_1
∀[n:ℕ+]. ∀[f:Top]. (f^n ~ λx.(f (f^n - 1 x)))
Proof
Definitions occuring in Statement :
fun_exp: f^n,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
lambda: λx.A[x],
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
false: False,
guard: {T},
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
compose: f o g
Lemmas referenced :
fun_exp_unroll,
nat_plus_subtype_nat,
top_wf,
nat_plus_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
sqequalAxiom,
setElimination,
rename,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[f:Top]. (f\^{}n \msim{} \mlambda{}x.(f (f\^{}n - 1 x)))
Date html generated:
2017_04_14-AM-07_34_21
Last ObjectModification:
2017_02_27-PM-03_07_29
Theory : fun_1
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